Problem: Simplify the following expression: $r = \dfrac{3}{8t + 3} \div \dfrac{7}{3t}$
Dividing by an expression is the same as multiplying by its inverse. $r = \dfrac{3}{8t + 3} \times \dfrac{3t}{7}$ When multiplying fractions, we multiply the numerators and the denominators. $r = \dfrac{ 3 \times 3t } { (8t + 3) \times 7}$ $r = \dfrac{9t}{56t + 21}$